To test this assumption, we generalized the roughness measure introduced by Aita, Ikamura and Husimi in [1]}. More precisely, we measured deviations from fitness additivity (in the language of the NK model, we say that a landscape is additive when it is non-epistatic, that is, \(K=0\) ).
We here use the term roughness from  [1]} to distinguish this measure, which is a local one, from the classical ruggedness of the NK-fitness landscape which is a global property of the landscape.
See, for example, Refs. [3]} and [4]}, for other definitions of roughness and how they are calculated.
Following the approach introduced in [1]}, we computed the roughness of the fitness landscape as the root mean square fitness variation due to each possible mutation, for both point mutations and inversions (see Sec:Methods for a formal mathematical definition of this measure).
The results are shown in Fig REF .
As expected, for point mutations the roughness of the fitness landscape is (almost) linearly proportional to the epistatic interaction parameter \(K\) , for both types of epistatic interaction neighborhoods (adjacent and random).
In contrast, in the case of inversion mutations, the roughness is always greater than that of point mutations, this trend being particularly visible for random epistatic neighborhood when compared to adjacent neighborhood. Interestingly, even for \(K=0 \) , the roughness is already higher than for point mutations (both epistatic neighborhood being equivalent in that case) while for \(K=N-1\)  the roughness converges approximately towards similar values both for inversions and point mutations whatever the epistatic neighborhood.
